Measurement Scales (Statistics)

In summary: Thanks for your answer tiny- tim, the way I think about discrete is that it has limited values and gaps in between those values ( like shoe size). Discrete can have decimal places . Whereas, in continuous you can have a unlimited values. Is it right for me to say that if I can take any 2 numbers and get a number in between that it's continuous? For example, taking time for instance I can say its 3:01 or 3:02 and any time in between I can get, so therefore it would be continuous. if discrete can only take limited values, like shoe size, then time of day can't be continuous because it has an unlimited number of values that could be included.the
  • #1
Cudi1
98
0

Homework Statement


In class we have to determine whether something is nominal, ordinal, interval or ratio and with the last 2 (ratio/interval) you have to state if they are discrete or continuous.


Homework Equations


n/a


The Attempt at a Solution


Height of Mt Everst above Sea level= interval continuous
What is your shoe size? - ratio discrete
What time of day did the red car finish the race? - ratio continuous
hand span in cm? ratio continuous
heigh in inches? ratio continuous

I'm very confused because discrete can only take limited values whereas continuous can take any number of values. I'd appreciate your help greatly. Thank you
 
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  • #2
Hi Cudi1! :smile:

How can time of day be ratio? :confused:

As to discrete and continuous, according to unesco at http://www.unesco.org/webworld/idams/advguide/Chapt1_3.htm all interval and ratio measurements are continuous. :confused:

(http://en.wikipedia.org/wiki/Level_of_measurement, although good, doesn't help on this issue)
 
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  • #3
Thanks for your answer tiny- tim, the way I think about discrete is that it has limited values and gaps in between those values ( like shoe size). Discrete can have decimal places . Whereas, in continuous you can have a unlimited values. Is it right for me to say that if I can take any 2 numbers and get a number in between that it's continuous? For example, taking time for instance I can say its 3:01 or 3:02 and any time in between I can get, so therefore it would be continuous.

To be honest , I discussed with my friend and he said time of day can't be ratio continuous cause time is used as a reference point, rather its interval continuous. Could you explain how it is though?
 
  • #4
As well, do the others look correct? I understand time of day is incorrect but don't know why:s . thanks
 
  • #5
Hi Cudi1! :smile:
Cudi1 said:
Thanks for your answer tiny- tim, the way I think about discrete is that it has limited values and gaps in between those values ( like shoe size). Discrete can have decimal places . Whereas, in continuous you can have a unlimited values. Is it right for me to say that if I can take any 2 numbers and get a number in between that it's continuous? For example, taking time for instance I can say its 3:01 or 3:02 and any time in between I can get, so therefore it would be continuous.

my understanding from the above unesco link is that "continuous" includes measurements that are rounded

eg that we measure height to the nearest cm, or age to the nearest year, but that's still continuous (we can't measure anything exactly, can we? o:))

when "discrete" refers to numbers, it means numbers that are not quantitative measurements, such as the uneven age groups 1 to 5 in the link

i think :redface:
Cudi1 said:
I understand time of day is incorrect but don't know why:s . thanks
I discussed with my friend and he said time of day can't be ratio continuous cause time is used as a reference point, rather its interval continuous. Could you explain how it is though?

finishing the race at 2 o'clock isn't twice as anything as finishing the race at 1 o'clock …

the ratio is irrelevant, since it depends when you start the clock …

so this isn't ratio

(the time to complete the course, from start to finish, would be ratio)
 

1. What are the different types of measurement scales in statistics?

There are four main types of measurement scales in statistics: nominal, ordinal, interval, and ratio. Nominal scales are used to label and categorize data, without any numerical value. Ordinal scales have categories that can be ranked in a specific order, but the intervals between these categories are not equal. Interval scales have equal intervals between categories, but do not have a true zero point. Ratio scales have equal intervals and a true zero point, allowing for meaningful ratios between measurements.

2. How do you determine which measurement scale to use for a specific data set?

The measurement scale to use depends on the type of data being collected and the type of analysis that will be performed. Nominal scales are best for categorical data, ordinal scales are suitable for data with ranked categories, interval scales are used for numerical data without a true zero point, and ratio scales are appropriate for numerical data with a true zero point. It is important to consider the characteristics of the data and the research question when selecting a measurement scale.

3. Can data be converted from one measurement scale to another?

In some cases, data can be converted from one measurement scale to another. For example, ordinal data can be converted to interval data by assigning numerical values to the categories, such as 1 for low, 2 for medium, and 3 for high. However, this conversion may not always be appropriate and can result in the loss of information. It is important to carefully consider the nature of the data and the research question before attempting to convert measurement scales.

4. What is the significance of using appropriate measurement scales in statistical analysis?

The use of appropriate measurement scales is crucial in statistical analysis as it impacts the validity and reliability of the results. Using an incorrect measurement scale can lead to incorrect conclusions and misleading interpretations of the data. It is important to carefully select the appropriate measurement scale in order to accurately analyze and interpret the data.

5. Are there any limitations to measurement scales in statistics?

Yes, there are limitations to measurement scales in statistics. For example, nominal scales do not allow for numerical calculations, and ordinal scales do not have equal intervals between categories. Interval and ratio scales assume equal intervals between categories, which may not always be the case. Additionally, the selection of a measurement scale is often subjective and can vary between researchers, potentially leading to different conclusions. It is important to be aware of these limitations and choose the most appropriate measurement scale for the specific data and research question.

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